What is the rest of the question
Answer:
The amount of oil was decreasing at 69300 barrels, yearly
Step-by-step explanation:
Given
![Initial =1\ million](https://tex.z-dn.net/?f=Initial%20%3D1%5C%20million)
![6\ years\ later = 500,000](https://tex.z-dn.net/?f=6%5C%20years%5C%20later%20%3D%20500%2C000)
Required
At what rate did oil decrease when 600000 barrels remain
To do this, we make use of the following notations
t = Time
A = Amount left in the well
So:
![\frac{dA}{dt} = kA](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%20%3D%20kA)
Where k represents the constant of proportionality
![\frac{dA}{dt} = kA](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%20%3D%20kA)
Multiply both sides by dt/A
![\frac{dA}{dt} * \frac{dt}{A} = kA * \frac{dt}{A}](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%20%2A%20%5Cfrac%7Bdt%7D%7BA%7D%20%3D%20kA%20%2A%20%5Cfrac%7Bdt%7D%7BA%7D)
![\frac{dA}{A} = k\ dt](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7BA%7D%20%20%3D%20k%5C%20dt)
Integrate both sides
![\int\ {\frac{dA}{A} = \int\ {k\ dt}](https://tex.z-dn.net/?f=%5Cint%5C%20%7B%5Cfrac%7BdA%7D%7BA%7D%20%20%3D%20%5Cint%5C%20%7Bk%5C%20dt%7D)
![ln\ A = kt + lnC](https://tex.z-dn.net/?f=ln%5C%20A%20%3D%20kt%20%2B%20lnC)
Make A, the subject
![A = Ce^{kt}](https://tex.z-dn.net/?f=A%20%3D%20Ce%5E%7Bkt%7D)
i.e. At initial
So, we have:
![A = Ce^{kt}](https://tex.z-dn.net/?f=A%20%3D%20Ce%5E%7Bkt%7D)
![1000000 = Ce^{k*0}](https://tex.z-dn.net/?f=1000000%20%3D%20Ce%5E%7Bk%2A0%7D)
![1000000 = Ce^{0}](https://tex.z-dn.net/?f=1000000%20%3D%20Ce%5E%7B0%7D)
![1000000 = C*1](https://tex.z-dn.net/?f=1000000%20%3D%20C%2A1)
![1000000 = C](https://tex.z-dn.net/?f=1000000%20%3D%20C)
![C =1000000](https://tex.z-dn.net/?f=C%20%3D1000000)
Substitute
in ![A = Ce^{kt}](https://tex.z-dn.net/?f=A%20%3D%20Ce%5E%7Bkt%7D)
![A = 1000000e^{kt}](https://tex.z-dn.net/?f=A%20%3D%201000000e%5E%7Bkt%7D)
To solve for k;
![6\ years\ later = 500,000](https://tex.z-dn.net/?f=6%5C%20years%5C%20later%20%3D%20500%2C000)
i.e.
![t = 6\ A = 500000](https://tex.z-dn.net/?f=t%20%3D%206%5C%20A%20%3D%20500000)
So:
![500000= 1000000e^{k*6}](https://tex.z-dn.net/?f=500000%3D%201000000e%5E%7Bk%2A6%7D)
Divide both sides by 1000000
![0.5= e^{k*6}](https://tex.z-dn.net/?f=0.5%3D%20e%5E%7Bk%2A6%7D)
Take natural logarithm (ln) of both sides
![ln(0.5) = ln(e^{k*6})](https://tex.z-dn.net/?f=ln%280.5%29%20%3D%20ln%28e%5E%7Bk%2A6%7D%29)
![ln(0.5) = k*6](https://tex.z-dn.net/?f=ln%280.5%29%20%3D%20k%2A6)
Solve for k
![k = \frac{ln(0.5)}{6}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7Bln%280.5%29%7D%7B6%7D)
![k = \frac{-0.693}{6}](https://tex.z-dn.net/?f=k%20%3D%20%5Cfrac%7B-0.693%7D%7B6%7D)
![k = -0.1155](https://tex.z-dn.net/?f=k%20%3D%20-0.1155)
Recall that:
![\frac{dA}{dt} = kA](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%20%3D%20kA)
Where
= Rate
So, when
![A = 600000](https://tex.z-dn.net/?f=A%20%3D%20600000)
The rate is:
![\frac{dA}{dt} = -0.1155 * 600000](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%20%3D%20-0.1155%20%2A%20600000)
![\frac{dA}{dt} = -69300](https://tex.z-dn.net/?f=%5Cfrac%7BdA%7D%7Bdt%7D%20%3D%20-69300)
<em>Hence, the amount of oil was decreasing at 69300 barrels, yearly</em>
Answer:jio
Step-by-step explanation:
Answer:
![Depth = 14.9\ metres](https://tex.z-dn.net/?f=Depth%20%3D%2014.9%5C%20metres)
Step-by-step explanation:
Given
![Desc = 20.6\ metres](https://tex.z-dn.net/?f=Desc%20%3D%2020.6%5C%20metres)
![Asc = 5\frac{7}{10}\ metres](https://tex.z-dn.net/?f=Asc%20%3D%205%5Cfrac%7B7%7D%7B10%7D%5C%20metres)
Required
Determine the depth
The depth is the distance between the two distances as follows'
![Depth = |Desc - Asc|](https://tex.z-dn.net/?f=Depth%20%3D%20%7CDesc%20-%20Asc%7C)
Substitute values
![Depth = |20.6 - 5\frac{7}{10}|](https://tex.z-dn.net/?f=Depth%20%3D%20%7C20.6%20-%205%5Cfrac%7B7%7D%7B10%7D%7C)
Convert fraction to decimal
![Depth = |20.6 - 5.70|](https://tex.z-dn.net/?f=Depth%20%3D%20%7C20.6%20-%205.70%7C)
![Depth = |14.9|](https://tex.z-dn.net/?f=Depth%20%3D%20%7C14.9%7C)
![Depth = 14.9\ metres](https://tex.z-dn.net/?f=Depth%20%3D%2014.9%5C%20metres)
Answer:
A function has no x values repeated twice.